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{{context|date=July 2012}} | |||
In physics, in the context of [[M-theory]], the [[Action (physics)|action]] for the [[Supersymmetry|N]]=8 M2 [[branes]] in full is (with some indices hidden): | |||
:<math> | |||
S = \int{ \left( -\frac{1}{2} D^\mu X_I D_\mu X_I +\frac{i}{2} \overline{\Psi} \Gamma^\mu D_\mu \Psi +\frac{i}{4} \overline{\Psi} \Gamma_{IJ} \left[ X^I, X^J, \Psi \right] - \frac{1}{12} \left[ X^I, X^J, X^K \right] \left[ X^I, X^J, X^K \right] + \frac{1}{2}\varepsilon^{abc}Tr(A_a\partial_b A_c + \frac{2}{3}A_a A_b A_c)\right) }d\sigma^3 | |||
</math> | |||
where [, ] is a generalisation of a [[Lie bracket]] which gives the group constants. | |||
The only known compatible solution however is: | |||
:<math> | |||
\left[A,B,C\right]_\eta \equiv \varepsilon^{\mu\nu\tau\eta}A_\mu B_\nu C_\tau | |||
</math> | |||
using the [[Levi-Civita symbol]] which is invariant under [[SO(4)]] rotations. M5 branes can be introduced by using an infinite [[symmetry group]]. | |||
The action is named after Jonathan Bagger, Neil Lambert, and Andreas Gustavsson.<ref>J. Bagger and N. Lambert, Modeling multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108]</ref><ref>A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260]</ref> | |||
==Notes== | |||
{{reflist}} | |||
==References== | |||
*[http://arxiv.org/abs/0804.2110v2 ''Lie 3-Algebra and Multiple M2-branes''] | |||
{{DEFAULTSORT:Bagger-Lambert-Gustavsson action}} | |||
[[Category:String theory]] | |||
{{string-theory-stub}} | |||
Revision as of 00:14, 21 March 2013
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In physics, in the context of M-theory, the action for the N=8 M2 branes in full is (with some indices hidden):
where [, ] is a generalisation of a Lie bracket which gives the group constants.
The only known compatible solution however is:
using the Levi-Civita symbol which is invariant under SO(4) rotations. M5 branes can be introduced by using an infinite symmetry group.
The action is named after Jonathan Bagger, Neil Lambert, and Andreas Gustavsson.[1][2]
Notes
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